Question

Carlos is drawing a trend line on his scatter plot that goes through the points (10, 3) and (7, 9). What is the equation of the line?

Answer 1

To find the equation of the line, calculate the slope from the two given points and then use one of the points to solve for the y-intercept. The equation of Carlos's trend line through the points (10, 3) and (7, 9) is y = -2x + 23.

Step-by-step explanation:

To find the equation of the line that goes through the points (10, 3) and (7, 9), we first need to calculate the slope of the line (m), which can be found using the formula m = (y2 - y1) / (x2 - x1). For our points (10, 3) and (7, 9), the slope calculation would be m = (9 - 3) / (7 - 10) = 6 / -3 = -2. Once we have the slope, we can use one of the points to find the y-intercept (b) using the formula y - mx = b. Using the point (10, 3) and the slope -2, we plug these into the formula: 3 - (-2)(10) = b, which simplifies to b = 3 + 20 = 23.

Now we have both the slope and the y-intercept needed to write the equation of the line in the slope-intercept form, y = mx + b. With m = -2 and b = 23, the equation of Carlos's trend line is y = -2x + 23.

Answer 2

Answer:To find the equation of the line that passes through the points (10, 3) and (7, 9), we can use the slope-intercept form of a line, which is given by the equation y = mx + b. In this form, m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.

To find the slope of the line, we can use the formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the coordinates of the two points, we get:

m = (9 - 3) / (7 - 10)

Simplifying, we get:

m = 6 / -3

So the slope of the line is -2.

To find the y-intercept, we can use one of the given points and substitute the values for x and y into the equation y = mx + b. For example, we can use the point (10,3):

3 = -2(10) + b

Solving for b, we get:

b = 23

So the equation of the line that passes through the points (10, 3) and (7, 9) is:

y = -2x + 23

This is the final answer.

Step-by-step explanation: that was the explanation